Question

A particle is projected with velocity 10m/s at an angle of 60° from ground . then the vertical component of velocity vector when instantaneous velocity becomes perpendicular to initial velocity is​

Answer 1

Answer:

The vertical component when the velocity will be perpendicular will be 10(sin60)*t + 1/2gt^2 and the horizontal component will be 10cos60.

So, we know that the 10cos60/10(sin60)*t + 1/2gt^2  = tan60.

Thus, we will get 10(cos60)^2 = 10(sin60)^2*t + 1/2gsin60*t^2.

On solving we will get  10*1/4 = 10*3/4*t + 5*√3/2t^2.

Which on simplifying we will get t= 5(sin60 + √(1+cot^2(60))

Then, t=5(√3/2 + 2/√3).

Which will approximately be equal to 10 seconds.